Al-Jazeera TV aired the tape, dated Jan. 21, showing Canadians James Loney and Harmeet Singh Sooden, along with an American and a British co-worker.
The four members of the Christian Peacemaker Teams disappeared in Baghdad on Nov. 26.
The video — which is grey and apparently shot using the camera's night-vision function — shows the four men standing near a wall, before cutting to another shot in which they are seated and talking, but their voices are not heard.
At one point, Mr. Loney is seen close-up, wearing a tuque and speaking into the camera, and he looked relatively fine, said the CPT's William Payne, a friend of Loney's.
"My immediate reaction was he looked well considering the circumstances and I was really happy," Payne said at a Toronto news conference Saturday afternoon. "He seemed himself from his facial expressions."
The Loney family awoke to the news Saturday morning and said they were encouraged to see James is still alive.
Mr. Loney's brother, Matt Loney, first heard about the video sometime around 6 a.m., local time, in Vancouver and said that while it was good to see his brother, it's still not the best of news.
"It's a good and bad scenario. We know that he's alive and the others are alive as well, and we take great solace in that fact," he said.
"But the fact remains that this is still a delicate situation."
Mr. Loney's mother was happy to see her son again, even under the difficult circumstances, said the CPT's Rebecca Johnson.
"Mrs. Loney was also relieved to see her son is alive and happy to see that — that was one of the first things she said," according to Ms. Johnson.
"(The family) is hoping for the best and for his release, of course."
The previously unknown Swords of Righteousness Brigades claimed responsibility for the kidnappings and called it a "last chance" for the hostages. They demanded the release of all Iraqi prisoners "otherwise their fate will be death" although no deadline was set.
There had been no word on the fate of Mr. Loney, 41, of Toronto, Mr. Sooden, 32, a former Montreal resident, Tom Fox, 54, of Clear Brook, Va., and Norman Kember, 74, of London, since the last deadline expired on Dec. 10.
Government spokesman Dan McTeague said Saturday that freeing the hostages remains a priority.
"All the resources of the government of Canada have been co-ordinated to communicate and listen to and receive any information that would help us see the safe release of these hostages," Mr. McTeague said.
"We will continue to emphasize to the hostage-takers that these are individuals that went there out of profound respect for the Iraqi people and Islam."
Christian Peacemaker Teams has been working in Iraq since October 2002, investigating allegations of abuse against Iraqi detainees by American and Iraqi forces. Its teams host human rights conferences in conflict zones, promoting peaceful solutions.
The group said it was grateful and heartened to see the hostages alive.
"They don't look ill-treated so we expect they're being cared for and that's very reassuring to us," Ms. Johnson said.
"We pray that those who hold them will host them with the grace that so many of us in CPT have received as guests in Iraq. James, Harmeet, Norman and Tom are peace workers who have not collaborated with the occupation of Iraq and who have worked for justice for all Iraqis, especially those detained."
Humanitarian workers had been warned repeatedly by Iraqi and western security officials that they were taking a grave risk if they moved around Baghdad without bodyguards.
More than 250 foreigners have been taken hostage in Iraq since the 2003 U.S.-led invasion that toppled Saddam Hussein, and at least 39 have been killed.
Among the hostages still unaccounted for is American reporter Jill Carroll, 28, who was abducted Jan. 7 in Baghdad. Her kidnappers have demanded the release of all Iraqi women in custody.
The U.S. military said this week's release of five Iraqi women from military custody was coincidental and not in response to the ultimatum.
Another member of CPT, retired Ontario dairy farmer Allan Slater, returned to Baghdad this month.
Mr. Slater, 70, is a friend of Mr. Loney's, and before he left Canada, he said he hopes this trip will be a reunion.
"When these people are released — and I believe they will be — they will be dumped onto the streets of Baghdad and the only place they will have to go is back to our apartment. We have to have someone there," Mr. Slater said.
Al-Jazeera editor Saad al-Dosari declined to say how the station obtained the tape.